Let A be an algebra and let X be an A-bimodule. A C−linear mapping d : A → X is called a generalized Jordan derivation if there exists a Jordan derivation (in the usual sense) δ : A → X such that d(a) = ad(a) + δ(a)a for all a ∈ A. The main purpose of this paper to prove the Hyers-Ulam-Rassias stability and superstability of the generalized Jordan derivations.

Very recently, Agarwal et al. (Fixed Point Theory Appl. 2012:40, 2012) initiated the study of fixed point theorems for mappings satisfying cyclical generalized contractive conditions in complete partial metric spaces. In the present paper, we study some fixed point theorems for a mapping satisfying a cyclical generalized contractive condition based on a pair of altering distance functions in co...

In this paper, a generalized KdV equation with time-dependent coefficients will be studied. The K(m,n) equation with generalized evolution will also be examined. The Riccati equation mapping method will be used to obtain some new exact solutions for both equations. These solutions include solitary wave solutions and periodic wave solutions. The results presented in this paper improve the previo...

In this paper we present an easy computation of a generalized form of barycentric coordinates for irregular, convex n-sided polygons. Triangular barycentric coordinates have had many classical applications in computer graphics, from texture mapping to ray-tracing. Our new equations preserve many of the familiar properties of the triangular barycentric coordinates with an equally simple calculat...

We establish a mapping of a general spin-fermion system in one dimension into a classical generalized Coulomb gas. This mapping allows a renormalization-group treatment of the anisotropic Kondo chain both at and away from half-filling. We find that the phase diagram contains regions of paramagnetism, partial, and full ferromagnetic order. We also use the method to analyze the phases of the Isin...

In the present article, certain classes of generalized p-valent Robertson functions are considered. Mapping properties of these classes are investigated under certain p-valent integral operators introduced by Frasin recently.

Interpreting metaphors is an integral and inescapable process in human understanding of natural language. This paper discusses a method of analyzing metaphors based on the existence of a small number of generalized metaphor mappings. Each generalized metaphor contains a recognition network, a basic mapping, additional transfer mappings, and an implicit intention component. It is argued that the...

In this paper, we establish the existence of a fixed point for generalized nonexpansive multivalued mappings in hyperbolic spaces and we prove some [Formula: see text]-convergence and strong convergence theorems for the iterative scheme proposed by Chang et al. (Appl Math Comp 249:535-540, 2014) to approximate a fixed point for generalized nonexpansive multivalued mapping under suitable conditi...

Let VIP(F; C) denote the variational inequality problem associated with the mapping F and the closed convex set C. In this paper we introduce weak conditions on the mapping F that allow the development of a convergent cutting-plane framework for solving VIP(F; C). In the process we introduce, in a natural way, new and useful notions of generalized monotonicity for which rst order characterizati...